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A053698
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a(n) = n^3 + n^2 + n + 1.
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36
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1, 4, 15, 40, 85, 156, 259, 400, 585, 820, 1111, 1464, 1885, 2380, 2955, 3616, 4369, 5220, 6175, 7240, 8421, 9724, 11155, 12720, 14425, 16276, 18279, 20440, 22765, 25260, 27931, 30784, 33825, 37060, 40495, 44136, 47989, 52060, 56355, 60880
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OFFSET
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0,2
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COMMENTS
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a(n) = 1111 in base n.
n^3 + n^2 + n + 1 = (n^2 + 1)*(n + 1), therefore a(n) is never prime. - Alonso del Arte, Apr 22 2014
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Colin Barker, Jan 02 2017
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EXAMPLE
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a(2) = 15 because 2^3 + 2^2 + 2 + 1 = 8 + 4 + 2 + 1 = 15.
a(3) = 40 because 3^3 + 3^2 + 3 + 1 = 27 + 9 + 3 + 1 = 40.
a(4) = 85 because 4^3 + 4^2 + 4 + 1 = 64 + 16 + 4 + 1 = 85.
The terms of the sequence are provided by the row sums of the following triangle (see the seventh formula in the previous section):
. 1;
. 3, 1;
. 9, 5, 1;
. 19, 13, 7, 1;
. 33, 25, 17, 9, 1;
. 51, 41, 31, 21, 11, 1;
. 73, 61, 49, 37, 25, 13, 1;
. 99, 85, 71, 57, 43, 29, 15, 1;
. 129, 113, 97, 81, 65, 49, 33, 17, 1;
. 163, 145, 127, 109, 91, 73, 55, 37, 19, 1;
. 201, 181, 161, 141, 121, 101, 81, 61, 41, 21, 1;
...
(End)
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MAPLE
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MATHEMATICA
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PROG
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(PARI) Vec((1 + 5*x^2) / (1 - x)^4 + O(x^50)) \\ Colin Barker, Jan 02 2017
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CROSSREFS
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Cf. A237627 (subset of semiprimes).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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